Product of Exponential Formula of Multidual Quaternions and Higher-Order Kinematics

A novel computational method of higher-order kinematics motion of multibody systems of rigid bodies is proposed in this paper. A crucial observation of the new approach is the generic properties of the automatic differentiation feature of extended function in multidual (MD) algebra. A specific diffe...

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Bibliographic Details
Published in2023 9th International Conference on Control, Decision and Information Technologies (CoDIT) pp. 537 - 542
Main Author Condurache, Daniel
Format Conference Proceeding
LanguageEnglish
Published IEEE 03.07.2023
Subjects
Algebra
Calculus
End effectors
Higher-order kinematics
Kinematics
multidual quaternions
POE formula
Quaternions
Resists
Transforms
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Summary:A novel computational method of higher-order kinematics motion of multibody systems of rigid bodies is proposed in this paper. A crucial observation of the new approach is the generic properties of the automatic differentiation feature of extended function in multidual (MD) algebra. A specific differential transform represents a symbolic determination of field invariants in higher-order accelerations field. All information of this representation is encapsulated in a quaternion definite in the tensorial product on dual and multidual algebras, denoted hyper-multidual (HMD) algebra. In the case of a lower-pair kinematic serial chain, a Product of the Exponential (POE) formula of HMD quaternion of the end-effector of the spatial kinematic chain in HMD algebra is presented in various reference frames.
ISSN:2576-3555
DOI:10.1109/CoDIT58514.2023.10284240